This is in a Linux VM image on Win 7.
The listener is up and the database appears to be up.
I, "su - oracle" and the the various env var are set.
I have the various groupid's setup and oracle is a member of them.
I also did a, "ssh systemname", to verify the login passwd.
oracle is in the sudo file.
I have uninstalled and installed a few times.
Restarting the Linux image does seem to start Oracle and the TNS listener.
I've tried sqlplus login with oracle, sys, system and as sysdba. I've checked my group id's and it contains: oracle, dba, oinstall, oper.
The files all have 755 and owned by oracle:dba.
I have searched all over the web and I have not been able to find anything that helps.
Any help would be great!

This is usally the case when you've either actually entered the wrong password, or your password contains "invalid" characters, such as the @-sign.

I've tried sqlplus login with oracle, sys, system and as sysdba. I've checked my group id's and it contains: oracle, dba, oinstall, oper.

It seems you have more than just an XE install in your VM, as "oinstall" and "oper" are usually not created by the XE installer.
Possibly, there are a few other environment variables that don't fit to your XEs ORACLE_HOME...
You should also try to make "dba" the primary group of your oracle user.

My password is a total of 9 characters, of which two are numbers. No punctuation or special characters.
My default group id is dba. If I do a, "touch x", it is owned by oracle:dba.
No, that's it, I just have Oracle XE installed. I added the other groups to make sure I covered my bases.

If I can perform a, "sqlplus /nolog" okay, does that indicate that the Oracle database is up? I believe the listener is working okay.

Just found out I missed one piece here: The user "sys" can't login with a default role, but needs to login as "SYSDBA". Try

conn sys/passwd@xe as sysdba

instead.

If I can perform a, "sqlplus /nolog" okay, does that indicate that the Oracle database is up?

No, it just means you start sqlplus.This alone does not connect you to any database.

I believe the listener is working okay.

I think so too, as you say you are able to access APEX. This would also mean that your database is up.

So, this leaves us with...

sqlplus / as sysdba
ERROR:
ORA-01031: insufficient privileges

My default group id is dba. If I do a, "touch x", it is owned by oracle:dba.

... where the questions would be:
- Have you really been logged in with "oracle" and being member of group dba when you received this?
- Has your environment actually been set properly at this moment?
- Are you sure you haven't disabled OS authentication?

When I tried the browser, I was able to bring up the Oracle Application Express admin login, but I was not able to login. http://hostname:8080/apex/apex_admin
I received an, "Invalid Login Credentials".

Probably you either connect to a different dabase instance you actually enter a different password than the one you've entered in the installer.
To change it, you need to be able to login as sysdba, either with password or OS authentication.

The one thing that you mentioned was, OS authentication. I don't know if OS authentication is enabled or disabled.
My understanding is that you have to be able to login into sqlplus to be able to turn this on or off. In my case, I running a Linux vm image on Win 7.
My Linux 5 image is running stand alone and not using any system for authentication. My understanding is that Oracle XE is NOT using OS authentication by default, so that could be the issue here.

My understanding is that you have to be able to login into sqlplus to be able to turn this on or off.

On Linux, this is true. On Windows, you'd also have the sqlnet.ora in your network configuration.

My understanding is that Oracle XE is NOT using OS authentication by default, so that could be the issue here.

No, you should be able to use it after a fresh XE install - if everything went well.

In my case, I running a Linux vm image on Win 7.

The host OS should not be relevant, unless you've installed sqlplus on your host and you are actually trying to connect to the VM that way. If I didn't get you wrong, all your attempts have been locally, i. e. inside the VM.

How can I turn on OS authentication, if I can login with sqlplus?

So the login using

sqlplus sys/password@xe as sysdba

is working now?
If you didn't reconfigure anything in your instance yet, I'd still think there is some piece missing/wrong in your environment variables.
Could you post the output of

env | egrep 'PATH|ORA|LC|LANG|NLS'

And could you also check the install logs in /u01/app/oracle/product/11.2.0/xe/config/log ?

I see a failure here, but I doubt that is a problem:
postDBCreation.log"
begin
*
ERROR at line 1:
ORA-31112: fail to unregister for HTTP port using xdb configuration
ORA-06512: at "XDB.DBMS_XDB", line 528
ORA-06512: at "XDB.DBMS_XDB", line 667
ORA-06512: at line 2

Can someone let me know if the default Oracle XE Database install uses oracle database for the authentication? I doubt it tries to use OS authentication, by default.

When you execute this script, "/etc/init.d/oracle-xe configure", it suppose to setup the password you give it for the oracle, sys and system id's, right?
I hadn't tried it, but if you enter a 2nd passwd, that doesn't match the first, will the script catch that? I'm trying to figure out why the login or password does not match.
Now days, we consider it a security issue by telling you whether it is the login or passwd that is incorrect. I wish I could tell which one was the problem.